Circle

A circle is easy to make:
Draw a curve that is "radius" away
from a central point.
And so:
All points are the same distance
from the center.



Also, the circle is a plane shape (two dimensional). 
Definition
In fact the definition of a circle is "the set of all points on a plane that are a fixed distance from a center".
Radius and Diameter
The Radius is the distance from the center to the edge.
The Diameter starts at one side of the circle, goes through the center and ends on the other side.
So the Diameter is twice the Radius:
Diameter = 2 × Radius


Circumference
The Circumference is the distance around the edge of the circle.
It is exactly Pi (the symbol is π) times the Diameter, so:
Circumference = π × Diameter
And so these are also true:
Circumference = 2 × π × Radius
Circumference/Diameter = π 
Area
The area of a circle is π times the Radius squared, which is written:
A = π × r^{2}
Or, in terms of the Diameter:
A = (π/4) × D^{2}
It is easy to remember if you think of the area of the square that the circle would fit inside. 

Names
Because people have studied circles for thousands of years special names have come about.
Nobody wants to say "that line that starts at one side of the circle, goes through the center and ends on the other side" when a word like "Diameter" would do.
So here are the most common special names:

Lines
A line that goes from one point to another on the circle's circumference is called a Chord.
If that line passes through the center it is called a Diameter.
If a line "just touches" the circle as it passes it is called a Tangent.
And a part of the circumference is called an Arc. 
Slices
There are two main "slices" of a circle
The "pizza" slice is called a Sector.
And the slice made by a chord is called a Segment. 

Common Sectors
The Quadrant and Semicircle are two special types of Sector:

Quarter of a circle is called a Quadrant.
Half a circle is called a Semicircle. 

Inside and Outside

A circle has an inside and an outside (of course!). But it also has an "on", because you could be right on the circle.
Example: "A" is outside the circle, "B" is inside the circle and "C" is on the circle. 
